Seifert fibering surgery on periodic knots

Abstract

We show that if a periodic knot K in the 3-sphere yields a Seifert fibered manifold by Dehn surgery, then the quotient of K by the group action generated by any periodic map of K is a torus knot, except for a special case. We also consider what Seifert fibered manifolds are obtained by Dehn surgery on periodic knots. If a non-torus, periodic knot yields a Seifert fibered manifold M, then the base space of M is the 2-sphere; and some pair of exceptional fibers in M has indices coprime provided that M contains at most three exceptional fibers.